Enumerative sphere shaping for rate adaptation and reach increase in WDM transmission systems

Amari, Abdelkerim; Goossens, Sebastiaan; Gültekin, Yunus Can; Vassilieva, Olga; Kim, Inwoong; Ikeuchi, Tadashi; Okonkwo, Chigo; Willems, F.M.J.; Alvarado, Alex

doi:10.1049/cp.2019.0995

Cited by 14 publications

(14 citation statements)

References 8 publications

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“…We note that ( 16 ) converges to ( 12 ) for asymptotically optimum shaping architectures when

. Although the finite length information rate

in ( 16 ) is not an “achievable” rate in the strict sense, it has been employed to compare CCDM and ESS for the optical fibre channel in [ 61 , 62 , 63 ]. We note here that ( 16 ) is an instance of the rate expression (Equation (1) in [ 101 ]) provided for the layered PS architecture.…”

Section: Performance Comparisonmentioning

confidence: 99%

“…As for direct shaping methods, enumerative sphere shaping (ESS) and shell mapping (SM) are notable SpSh algorithms which are initially proposed in [ 22 , 59 ] respectively. ESS is recently considered in PAS framework [ 48 , 60 , 61 , 62 , 63 ], as well as SM in [ 64 ]. Furthermore, low-complexity implementation ideas for both of these algorithms have been presented in [ 65 ].…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

Gültekin

Fehenberger

Alvarado

et al. 2020

Entropy

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In this paper, we provide a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. However, as the blocklength decreases, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths over the additive white Gaussian noise (AWGN) channel, the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM) and SpSh are reviewed as energy-efficient shaping techniques. Numerical results show that both have smaller rate losses than CCDM. SpSh—whose sole objective is to maximize the energy efficiency—is shown to have the minimum rate loss amongst all, which is particularly apparent for ultra short blocklengths. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspectives of latency, storage and computations.

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“…We note that ( 16 ) converges to ( 12 ) for asymptotically optimum shaping architectures when

. Although the finite length information rate

Section: Performance Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

Gültekin

Fehenberger

Alvarado

et al. 2020

Entropy

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“…Probabilistic shaping based on distribution matching (DM) via constant composition (CC) [7], multiset partitioning [8], sphere shaping via shell mapping [9], and enumerative sphere shaping (ESS) [4], [10] has been considered in optical communication systems. A combination of probabilistic shaping and DBP have been also investigated in [11].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we propose to exploit the nonlinear tolerance gain that short block length ESS provides [4], [10], as a way to avoid the use of high complexity nonlinearity compensation techniques like DBP. We investigate the performance of uniform signaling with fiber nonlinearity compensation techniques and ESS with and without nonlinearity compensation, and explore the possibility of complexity reduction in this context.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Short Blocklength Sphere Shaping and Nonlinearity Compensation in WDM Systems

Amari

Lampe

Kumar

et al. 2020

IEEE Photon. Technol. Lett.

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In optical communication systems, short blocklength probabilistic enumerative sphere shaping (ESS) provides both linear shaping gain and nonlinear tolerance. In this work, we investigate the performance and complexity of ESS in comparison with fiber nonlinearity compensation via digital back propagation (DBP) with different steps per span. We evaluate the impact of the shaping blocklength in terms of nonlinear tolerance and also consider the case of ESS with a Volterra-based nonlinear equalizer (VNLE), which provides lower complexity than DBP. In single-channel transmission, ESS with VNLE achieves similar performance in terms of finite length bit-metric decoding rate to uniform signaling with one step per span DBP. In the context of a dense wavelength-division multiplexing (WDM) transmission system, we show that ESS outperforms uniform signaling with DBP for different step sizes.

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“…The gap is due to the use of uniform signaling with equidistant signal constellation points and the suboptimality of pragmatic FEC schemes. In order to enhance the performance of CM systems and reduce the two losses above, advanced FEC decoding architectures [ 3 , 4 , 5 , 6 ] and signal shaping [ 7 , 8 , 9 , 10 , 11 ] have received considerable attention in the optical communication literature. The most popular approach is to use a binary code mapped nonbinary constellation in a so-called bit-interleaved coded modulation (BICM) structure.…”

Section: Introductionmentioning

confidence: 99%

Hard-Decision Coded Modulation for High-Throughput Short-Reach Optical Interconnect

Chen

Lei

Liga

et al. 2020

Entropy

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Coded modulation (CM), a combination of forward error correction (FEC) and high order modulation formats, has become a key part of modern optical communication systems. Designing CM schemes with strict complexity requirements for optical communications (e.g., data center interconnects) is still challenging mainly because of the expected low latency, low overhead, and the stringent high data rate requirements. In this paper, we propose a CM scheme with bit-wise hard-decision FEC and geometric shaping. In particular, we propose to combine the recently introduced soft-aided bit-marking decoding algorithm for staircase codes (SCCs) with geometrically-shaped constellations. The main goal of this CM scheme is to jointly boost the coding gain and provide shaping gain, while keeping the complexity low. When compared to existing CM systems based on M-ary quadrature-amplitude modulation (MQAM, M = 64 , 128 , 256 ) and conventional decoding of SCCs, the proposed scheme shows improvements of up to 0 . 83 dB at a bit-error rate of 10 - 6 in the additive white Gaussian noise channel. For a nonlinear optical fiber system, simulation results show up to 24 % reach increase. In addition, the proposed CM scheme enables rate adaptivity in single-wavelength systems, offering six different data rates between 450 Gbit/s and 666 Gbit/s.

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Enumerative sphere shaping for rate adaptation and reach increase in WDM transmission systems

Cited by 14 publications

References 8 publications

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

Comparison of Short Blocklength Sphere Shaping and Nonlinearity Compensation in WDM Systems

Hard-Decision Coded Modulation for High-Throughput Short-Reach Optical Interconnect

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